NASA Technical Reports Server (NTRS) 19870012522: Unstalled flutter stability predictions and comparisons to test data for a composite prop-fan model

NASA CR-179512

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UNSTALLED FLUTTER STABILITY PREDICTIONS AND
COMPARISIONS TO TEST DATA FOR A COMPOSITE

PROP-FAN MODEL

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STABILITY P BE DICT IC NS AMD CCFPAEISCBS TO

TEST DATA EOB A COMPOSITE PECE-EAK MODEL

iinal Report (Haailtcn Standard) 50 p

Avail: NTIS HC AC3/Mf A01 CSCL 21E G3/07

W87-2 1S55

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0072744

J. E. Turnberg

HAMILTON STANDARD DIVISION
UNITED TECHNOLOGIES CORPORATION

October, 1986

Prepared For

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Lewis Research Center
Cleveland, Ohio 44135

Contact NAS3-24088

NASA CR-179512

NASA

UNSTALLED FLUTTER STABILITY PREDICTIONS AND
COMPARISIONS TO TEST DATA FOR A COMPOSITE

PROP-FAN MODEL

J. E. Turnberg

HAMILTON STANDARD DIVISION
UNITED TECHNOLOGIES CORPORATION

October, 1986

Prepared For

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Lewis Research Center
Cleveland, Ohio 44135

Contact NAS3-24088

V Report No. 2. Government Accession No.

CR-179512

3. Recipient's Catslog No.

4. Title and Subtitle

5. Report Date

Unstalled Flutter Stability Predictions and
Comparisons to Test Data for a Composite Prop-Fan
Model

October 15, 1986

6. Performing Organization Code

7. Authors)

6. Performing Organization Report No.

J. E. Turnberg

HSER 11056

10. Work Unit No.

9. Performing Organization Name and Address

Hamilton Standard Div., United Technologies Corp.
Windsor Locks, CT 06095

11. Contract or Grant No.

NAS3-24088 '

13. Type of Report and Period Covered

12. Sponsoring Agency Name and Address

National Aeronautics and Space Administration

Contractor

Lewis Research Center
21000 Brookpark Road
Cleveland, OH 44135

14. Sponsoring Agency Code

:

15. Supplementary Notes

Final Report. Technical Monitor - Mr. Oral Mehmed,

NASA - Lewis Research

Center, Cleveland, Ohio 44135

16. Abstract

This report presents the aeroelastic stability analyses for three graphite/epoxy
composite Prop-Fan designs and post-test stability analysis for one of the
designs, the SR-3C-X2. The study showed that Prop-Fan stability can be
effectively analyzed using the F203 modal aeroelastic stability analysis
developed at Hamilton Standard and that first mode torsion-bending coupling
has a direct effect on blade stability. Positive first mode torsion-bending
coupling is a destabilizing factor and the minimization of this parameter will
increase Prop-Fan stability. The study also showed that Prop-Fan stability
analysis using F203 is sensitive to the blade modal data used as input.
Calculated blade modal properties varied significantly with, the structural
analysis used, and these variations are reflected in the F203 calculations.

17. Key Words (Suggested by Authors))

Flutter, Prop-Fan, Blades, Propeller,
Aeroelastic

16. Distribution Statement

Unclassified, Unlimited

19. Security Classlf. (of this report)

Unclassified

20. Security Classlf. (of thl» page)

Unclassified

21. No. of pages

50

‘For sale by the National Technical Intormatlon Service. Springfield, Virginia 22161

NASA CR 179512

FOREWORD

The analytical and experimental work described in this report was
conducted through the joint effort of the NASA-Lewis Research Center
and the Hamilton Standard Divison of the United Technologies
Corporation under NASA contract NAS3-24088. Mr. Oral Mehmed of the
NASA Lewis Research Center was the Technical Monitor for the
contract.

All of the testing was performed in the NASA-Lewis 8x6 wind tunnel
under the direction of Mr. Mehmed. NASA-Lewis personnel provided
the structural finite element analytical model and modal data for
aeroelastic stability predictions and the test data for comparison
with analytical predictions. At Hamilton Standard,

Mr. Jay E. Turnberg and Ms. Karen S. Morrell conducted the
analytical predictions. Mr. Bennett M. Brooks was the
Hamilton Standard Project Manager.

precede pa* K0T

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NASA CR 179512

TABLE OF CONTENTS

Page

FOREWORD V

TABLE OF CONTENTS vii

1.0 SUMMARY 1

2 . 0 INTRODUCTION 3

3.0 DISCUSSION . . 5

3 . 1 Flutter Model Selection 5

3 . 2 Experiment Description 7

3 . 3 Analytical Predictions and Comparisons to Test . 8

4.0 CONCLUSIONS AND RECOMMENDATIONS 13

5.0 REFERENCES 15

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NASA CR 179512

1.0 SUMMARY

This report presents the aeroelastic stability analyses performed
for three graphite/epoxy composite Prop-Fan designs and the
post-test aeroelastic stability analysis for one of the designs,
the SR-3C-X2 . The major objective of this work was to assist
NASA-Lewis in the development of two advanced composite Prop-Fan
models, one that would be stable to high flight Mach numbers and
one that would be unstable at low flight Mach numbers. The stable
model, the SR-3C-3, was used for subsequent wind tunnel structural
response and stability verification testing. The unstable model,
the SR-3C-X2 , was subjected to wind tunnel tests in order to obtain
flutter data.

This aeroelastic stability study showed that Prop-Fan stability can
be effectively analyzed using the F203 modal aeroelastic stability
analysis developed at Hamilton Standard and that first mode torsion
bending coupling has a direct effect on blade stability. Control of
this coupling by composite ply-layer tailoring was the procedure
used to produce the stable SR-3C-3 and the unstable SR-3C-X2 models.

The study also revealed that the prediction of Prop-Fan stability
using the F203 aeroelastic analysis is sensitive to the blade modal
data used as input. Although finite element analysis methods were
used to calculate all of the blade modal data for this study,
differences in the detailed finite element analysis solution
procedures caused variations in the blade modal data that are
reflected in the F203 stability predictions.

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2.0 INTRODUCTION

The emergence of the Prop-Fan as a fuel conservative competitor to
the high bypass ratio turbofan has created new interest in
propeller technology development. Both analytical studies and wind
tunnel tests at Mach numbers between 0 . 7 and 0 . 8 have shown that
aerodynamic performance efficiencies of about 80 percent are
achievable for single-rotation Prop-Fans (SRP) and efficiencies as
high as about 89 percent are achievable for Counter-Rotating
Prop-Fans (CRP) (Reference 1) .

These high efficiencies have been accompanied by increasing
structural demands over those of conventional turbopropellers.
Prop-Fans have six or more swept, thin, low aspect ratio blades.
These blade characteristics increase the potential for an
aeroelastically unstable configuration. This potential was
confirmed during testing of a highly swept titanium model Prop-Fan
called SR-5 at the NASA Lewis Research Center in the spring of 1981
(Reference 2) . The SR-5 model Prop-Fan exhibited an unstalled
flutter instability at high Mach number.

The consequence of the SR-5 instability was a re-examination of the
unstalled flutter prediction methodology and the development of new
unstalled flutter calculation procedures specifically tailored to
meet the needs of the Prop-Fan (References 2, 3, 4, and 5). To
further investigate flutter in advanced turboprops and to verify
analytical procedures, test data in addition to the SR-5 model
Prop-Fan test data was required. This need for additional data
prompted the development and testing of the SR-3C-X2 model Prop-Fan.

The SR-3C-X2 is a graphite fiber/epoxy matrix composite model
Prop-Fan fabricated at the NASA Ames Research Center. It was
designed to flutter at a subsonic Mach number and was tested in the
NASA Lewis 8x6 wind tunnel. The aerodynamic performance of this
model had been previously established from a solid titanium version
of the configuration known as the SR-3 (Reference 6) . Unstalled
flutter has never been observed during wind tunnel tests of the
SR-3. In addition to the SR-3C-X2 flutter model, another
graphite/epoxy model was developed, designated the SR-3C-3, for
stable dynamic response testing. This model, as with the metal
SR-3, did not exhibit flutter.

This report is a summary of the flutter blade design selection
process, and post-test stability analysis and correlation with data.
The program has involved a joint effort between NASA-Lewis and
Hamilton Standard personnel. Hamilton Standard provided test and
data reduction support for the program in addition to aeroelastic
stability analysis for the model. NASA-Lewis provided finite
element analysis results for the aeroelastic stability analysis and
all hardware and test facilities, conducted the test, and supplied
both raw and reduced data.

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NASA CR 179512

ired by the NASA Advanced Turboprop Project
.e overall program to develop advanced turboprop

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3.0 DISCUSSION

3 . 1 Flutter Model Selection

One goal of this program was the development of two composite model
Prop-Fans with the geometry of an existing solid titanium model
called SR- 3 . Figure 1 shows the geometric characteristics of the
SR- 3 Prop-Fan. One of the composite models, the SR-3C-X2, was
designed to flutter at a low flight Mach number while the other,
the SR-3C-3 , was designed to be stable to a high Mach number so
that it could be tested for dynamic response on an isolated nacelle
(Reference 7) .

From previous internal work performed at NASA-Lewis and Hamilton
Standard it was determined that Prop-Fan flutter could be controlled
by altering the vibratory mode shapes of the blades. Two techniques
are generally suitable to alter blade mode shape. One involves
changes in the blade external geometry, as was performed to obtain a
stable design for the LAP SR-7 Prop-Fan (Reference 8) , and the
other involves changes in the internal shape or material
composition of the blade. Tailoring the composite material ply
orientation will alter the structural characteristics but not
change the external geometry and was the method selected by
NASA-Lewis to create the SR-3C models. An additional factor which
must be included in the analysis with either geometric or composite
tailoring is the effect of the blade retention and hub
flexibilities. For this study the retention and hub could be
considered rigid so the flexibilites were not included in the
analysis. In general full scale designs have bearing retentions
and flexible hubs that must be included in the mode shape and
frequency calculations for subsequent stability predictions.

The type of flutter examined for this study is a predominant first
mode flutter. This type of flutter is greatly influenced by blade
sweep, torsion-bending coupling in the first in vacuo mode, and the
aerodynamic coupling of the first in vacuo mode to higher in vacuo
modes (Reference 5) . A distinction is made here between in vacuo
modes and aerodynamically coupled modes. A flutter mode is an
aerodynamically coupled mode. Unsteady aerodynamic loads introduce
stiffness and damping into the structure which modify the
frequencies and mode shapes of the in vacuo structure and alter
blade stability. Therefore a Prop-Fan operating in a wind tunnel
or under flight conditions has mode shapes and frequencies that are
altered with each change in rotational speed, wind tunnel or flight
speed, and air density or altitude. The extent to which the air
interacts with the Prop-Fan is related to the mass, stiffness and
geometric properties of the Prop-Fan.

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NASA CR 179512

Blade sweep introduces a destabilizing unsteady aerodynamic force
component into the system when the first in vacuo mode shape of the
blade has zero or positive torsion-bending coupling. Torsion-
bending coupling is defined by:

A = ^ <i)'

where torsion (©) is defined as rotation of an airfoil cross
section about the line tangent to the geometric mid-chord sweep
curve shown in Figure 1. A positive sign is given for leading
edge-up rotation. Bending (h) is defined as the translation of the
mid-chord in the direction normal to the blade surface with a
positive sign convention for translation toward the airfoil face
(pressure) side, as. illustrated in Figure 2, and blade dimension
(b) is the semi-chord.

The natural tendency of an aft swept blade is to vibrate in the
first mode with positive torsion-bending coupling because of the
overhung tip mass introduced by sweep. This natural tendency to
vibrate in the first mode with positive torsion-bending coupling
can be altered by tailoring the composite ply orientation.

Therefore, to select high and low stability composite SR-3 models,
NASA-Lewis personnel examined a number of composite ply
configurations of which three were selected as candidates for
flutter analysis, the SR-2C-X2, SR-3C-3, and the SR-3C-X7. These
three configurations differed only in ply orientation. Of these
configurations, the SR-3C-X2 and the SR-3C-3 were built, so that
the structural analyses could be verified.

The material composition of these models is a layered build-up of
graphite prepreg unidirectional tape with each layer, or ply,
oriented in the following specified directions. Figure 3 shows the
nominal graphite ply fiber orientation for the three configurations
that were analyzed for flutter during the model selection process.
The SR-3C-X2 had a (-22.5°, 0°, 22.5°) ply lay-up that made the
model flexible in torsion and brought the first and second mode
natural frequencies close together. The SR-3C-3 had a (-45°, 0°,
45°) ply lay-up to provide increased torsional rigidity. The third
configuration, the SR-3C-X7, had a (-45°, 0°, 7.5°, 45°, 52.5°) ply
orientation that increased the frequency separation between modes 1
and 2, and uncoupled the bending and torsional motion in the first
mode. All three configurations were constructed with the same type
of epoxy matrix and graphite ply material so the mass distribution
remained nearly constant. The effect of the stiffness variation due
to ply orientation is shown by examination of the blade natural
frequencies in Table I and the blade mode shapes in Figures 4, 5,
and 6 .

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NASA CR 179512

A _ comparison of the displacement contours for the first mode in
Figures 4, 5, and 6 shows contours with decreasing slope for the
SR-3C-X2, SR-3C-3, and SR-3C-X7 models, respectively. The slope of
these displacement contour lines is indicative of the magnitude of
the torsion-bending coupling. A summary of the torsion-bending
coupling for the first mode is shown in Figure 7. At the blade
tip, where the greatest aerodynamic forces are encountered, the
SR-3C-X2 model is shown to have the greatest amount of
torsion-bending coupling and, therefore, should have the lowest
stability of the three configurations.

The predicted first mode damping for the three proposed composite
SR-3 model Prop-Fans, shown in Figure 8, indicated that the assumed
low stability of the SR-3C-X2 is supported by analysis. The
stability prediction, was performed for the three Prop-Fan
configurations rotating at 8636 RPM with sea level aerodynamic
conditions. The critical flutter velocities for the SR-3C-X2,
SR-3C-3 and the SR-3C-X7 are Mach 0.28, Mach 0.68 and greater than
Mach 1.0, respectively. A review of the stability predictions
showed that two Prop-Fan models, the SR-3C-X2, and the SR-3C-3,
would satisfy the requirements of this program and future programs.
That is to have both high and low stability composite Prop-Fan
models, with the geometric shape of the SR-3.

Although the SR-3C-3 model shows a critical flutter velocity of
Mach 0.68, it was selected to be the high stability model because
Mach 0.68 represents the critical flutter velocity at sea level
conditions. This is a lower critical flutter velocity than would
be anticipated during testing, since the model is run in a wind
tunnel with an equivalent altitude of approximately 6000 ft at Mach
0.8. ^ The decreased dynamic pressure in the wind tunnel increases
stability. Another reason why the SR-3C-3 was selected over the
SR-3C-X7 was because it had the potential, according to
calculations, to flutter at a Mach number outside the operating
range of the planned response test based on extrapolation of
calculated sea level stability to wind tunnel test condition so
that flutter data could be obtained in addition to high speed
response data. Further information regarding the high stability
model, the SR-3C-3, is found in Reference 7. The SR-3C-3 did not
flutter during testing. The stability analysis used for this study
is described in detail in Reference 3, and will be described in
general in Section 3.3. The remainder of the report will deal only
with the low stability model, the SR-3C-X2.

3 . 2 Experiment Description

The SR-3C-X2 model Prop-Fan was tested by NASA-Lewis personnel in
the NASA-Lewis 8x6-foot wind tunnel during October of 1983. The
0.61 m (2.04 ft) diameter model was mounted on an isolated nacelle
test rig with the thrust axis aligned with the freestream flow.

The experiment was conducted at freestream velocities from 0.36 to
0.75 Mach number, with rotor speeds up to 8000 RPM. The blades
were mounted in a hub which can be considered to be rigid. Signals
from blade mounted strain gages were recorded on FM analog magnetic
tape, and also were monitored during the test to identify the

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NASA CR 179512

stability boundary of the model. The model was tested in two rotor
configurations, first with eight blades and second with four blades
to investigate aerodynamic coupling effects between the blades at
flutter. Flutter occurred over a wide range of operating conditions
for both operating configurations. A detailed description of the
experiment and the results can be found in Reference 9 . The only,
data that will be presented here are those that will be used for
comparison to the analysis.

The SR-3C-X2 model fluttered in the first aerodynamically coupled
mode when operating over a wide range of Mach number and rotational
speed in both the eight and four bladed configurations. During
flutter all blades vibrated at the same frequency but at different
amplitudes and with a common predominate phase angle between
adjacent blades. The eight-bladed configuration fluttered with
either a 180° or 225° interblade phase angle or with both angles
simultaneously. While the four-bladed configuration fluttered with
a 180° interblade phase angle (Reference 9) .

The measured blade natural frequencies from spectral analysis of
wind tunnel strain data are given in the Campbell plot shown in
Figure 9, along with the COSMIC NASTRAN predicted blade natural
frequencies. There are substantial discrepancies between the
rotating measured and predicted frequencies for the modes. The
first mode frequency is greater than that predicted while the
second mode is lower than that predicted. The frequencies of the
third and fourth modes could not be ascertained from the test data
with any degree of accuracy. Comparison of non-rotating
calculations and static shake tests for the SR-3C-X2, Table II, do
not show the frequency discrepancies. The frequency calculations
are well within the range of the shake test data. Note that the
measured values show large blade-to-blade differences for all the
modes, indicating that the assembled model was somewhat mis-tuned
from a blade frequency standpoint.

A portion if not all of the frequency discrepancy between the
rotating measured and calculated first and second mode frequencies
is due to aerodynamic effects. The calculations were performed "in
vacuo", without including the influence of aerodynamics. The
measured wind tunnel data show a substantial aerodynamic effect.

The effect of aerodynamic forces on the blade natural frequency
will be addressed further when the stability predictions are
discussed.

3 . 3 Analytical Predictions and Comparisons to Test

The analytical stability predictions for the SR-3C-X2 model were
performed using the F203 aeroelastic stability analysis. Briefly,
the F203 aeroelastic stability analysis is a modal analysis that
was specifically tailored to model the structural and aerodynamic
complexities of the Prop-Fan. The complicated geometry of the
Prop-Fan is modeled using the torsion-bending coupling shown in
Figure 7. The unsteady 2D aerodynamics for the analysis are
modeled to account for sweep, compressibility, cascade effects, and

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NASA CR 179512

blade tip losses. The solution for the equations of motion takes
the form of a complex eigenvalue problem that yields frequency,
damping, and complex mode shapes for the system.

The analysis procedure took the following overall approach. First,
Hamilton Standard recommended to NASA for analysis three test
conditions where flutter occurred. NASA- Lewis approved the test
conditions and five cases were developed by NASA-Lewis for finite
element analysis to assess the prediction methodology. These five
cases plus the pre-test case are summarized in Table III.

NASA-Lewis supplied Hamilton Standard with finite element modal
data for the analysis cases and stability predictions were made by
Hamilton Standard using the modal data assuming two model rotor
configurations, eight blades and four blades, to investigate
aerodynamic coupling between the blades.

Three different finite element procedures were applied to the blade
to assess the effect of finite element procedure on stability
predictions. The three techniques are as follows: COSMIC NASTRAN

without steady aerodynamic loads (cases 1 and 2) , MSC NASTRAN
without steady aerodynamic loads (case 3) , and finally MSC NASTRAN
with steady aerodynamic loads (cases 4, 5, and 6) as summarized in
Table III. Cases 2, 3, and 4 form a consistent set of runs for
evaluating the sensitivity of stability to the finite element
analysis procedure for a single test operating condition.

The comparison between the two NASTRAN programs, COSMIC and MSC, was
performed to assess how differences in solution procedures and
element formulations alter the blade stability results. MSC
NASTRAN was also run using two procedures; one that accounted for
steady aerodynamic loads and the other did not account for the
steady aerodynamic loads. The effect of steady aerodynamic loads
is to deflect the blade into a new mean position, and as noted
previously, the blade mode shapes are directly related to the mean
position of the blade.

The choice of finite element procedure did yield substantial
variations in the modal data for cases 2,3, and 4 . These
variations are summarized by frequencies in Table IV and mode
shapes in Figure 10. For the three comparison cases (2, 3 and 4)
the predicted first mode frequency varies over a range of only
6.0%, but the amount of first mode torsion-bending coupling varies
from 0.09 to 0.36 at the 80% radial station. Variations of this
magnitude directly affected the subsequent stability predictions.

The MSC NASTRAN with airloads finite element procedure used on
cases 4, 5, and 6 is the most sophisticated. The calculations
include steady aerodynamic loads and geometric nonlinearities. It
was initially thought that this procedure would best represent the
blade structurally, but even this solution technique shows an
inconsistency. The predicted natural frequencies of modes 2 and 3
do not increase with rotational speed. Case 6 at 6400 RPM shows a
second mode frequency of 400 Hz, while case 5 at 7368 RPM shows a
decreased second mode frequency of 364 Hz. The MSC NASTRAN with
airloads analysis indicates that the frequency decreases with

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NASA CR 179512

increasing rotational speed, which is an unlikely phenomenon for
the primary modes of a Prop-Fan blade. This also is not supported
by test data for this blade or by the pre-test COSMIC NASTRAN
frequency predictions shown in Figure 9.

The stability predictions made using these modal data were
performed for an eight-bladed configuration and a four-bladed
configuration. It should be noted that the four-bladed SR-3C-X2
stability calculations, made using MSC NASTRAN with airloads finite
element calculations, contain steady airloads developed for the
eight-bladed configuration. Therefore, these four-blade stability
predictions contain a known approximation, eight-bladed steady
airloads. All stability predictions were performed using the first
six normal modes to represent the blades in the calculations.

Eight Bladed Comparisons - The six cases were analyzed in an
eight-bladed configuration for point-to-point comparison to test
results. Predicted first mode damping and frequency plots for
these cases are shown in Figures 11 through 16. The first mode is
predicted to go unstable for each case at the predicted point of
zero damping. The flutter Mach numbers and frequencies for this
configuration are listed in Table V and displayed in Figure 17.

In all cases the upper bound Mach number for blade stability was
under-predicted. The correlation between prediction and test data
varied for each case. To begin the discussion of the comparison
between prediction and test data, the results from the three modal
calculation procedures, case 2, case 3, and case 4, representing
the 6100 RPM, Mach 0.6 test run 879 will be examined.

The three calculations for this flutter point show a variation in
flutter Mach number from 0.45 to 0.55. The COSMIC NASTRAN, case 2,
results showed the lowest upper bound Mach number for blade
stability with a flutter Mach number of 0.45. This is an under-
prediction, of the tested flutter Mach numer of 0.60, by 25%.

The change to MSC NASTRAN, case 3, increased the predicted
stability to Mach 0.55, which is an 8% under-prediction. Finally,
the addition of steady aerodynamic loads to the MSC NASTRAN modal
calculations lowered the previous prediction to Mach 0.54, which is
a 10% under-prediction. The results show that predictions using
MSC NASTRAN modal data gave better correlation to test results than
the COSMIC NASTRAN modal data for this flutter point. Also, the
inclusion of steady aerodynamic loads in the modal data calculation
procedure produced a small change in predicted stability. The
overall under-prediction of stability may, in part, be due to the
exclusion of any structural damping in the calculations.

Structural damping increases blade stability.

A comparison of the point-to-point predictions using MSC NASTRAN
with airloads, cases 4, 5, and 6, to the test values shows that the
case 6 at 6400 RPM result produced the best correlation with test
data. The calculation is within 3% of the tested upper bound Mach
number for blade stability for run 985. As discussed previously,
the case 4 prediction at 6100 RPM is within 10% of the tested run
879 stability. Case 5 at 7368 RPM does not correlate well with the

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NASA CR 179512

test data, and the calculation is inconsistent with the other
predictions. Case 5 under-predicts the onset of blade instability,
for run 904, by 82%.

The inconsistencies in the stability predictions follow the
differences found in the modal data. Comparing the finite element
study cases 2, 3, and 4, representing run 879, case 2 had far more
torsion-bending coupling than cases 3 and 4, and therefore was
predicted to be less stable. For the point-to-point comparison
cases, the cause of deviation for case 5 is not clear, although it
was noted previously that the frequency predictions show a low
value for the second mode. This is not in agreement with any of
the other analytical results, or the test data. This indicates
that some problems specific to this modal calculation may exist.

Since the results from case 5 were out of agreement with the other
predictions, further investigation into the difference was
performed. A comparison was made between two test operating
conditions with tip helical Mach numbers of about 0.85. These two
conditions were case 5 at Mach 0.5 and 7386 RPM and case 6 at Mach
0.6 and 6400 RPM.

Constant tip helical Mach number was selected as a basis for the
comparison because this establishes similar aerodynamic velocity
distributions. Even though the aerodynamic conditions are similar
for these calculations, the stability predictions are grossly
different. Case 6 shows a first mode viscous damping ratio and
frequency prediction of -0.015 and 283 Hz, while case 5 shows a
first mode viscous damping ratio and frequency prediction of -0.11
and 287 Hz. More insight into the difference can be obtained when
the eigenvectors for the two conditions are examined, see Table VI.
Case 6 shows 15% coupling between modes one and two while case 5
shows 28% coupling between modes one and two. This increased
coupling is destabilizing and is due to modal differences arising
from the finite element results.

For the eight-bladed stability predictions, cascade effects were
important because of the close blade spacing. When blades are
closely spaced, the motion of an adjacent blade affects the
stability of the blade under investigation, therefore, the Prop-Fan
was analyzed as a system of eight identical blades. The eight
blades were allowed to vibrate in eight possible system modes with
the following inter-blade phase angles 0°, 45°, 90°, 135°, 180°,
225°, and 315°. The predicted least stable inter-blade phase angle
was generally 135°, as shown in Figure 18. The predicted angle
differs from the measured phase angle by sign. The measured
inter-blade phase angle was 225° or 180° which is equivalent to
minus 135° or 180 . The reason for the phase polarity difference
between the analysis and experiment is not presently understood and
warrants further investigation. The disagreement in inter-blade
phase angle between test and calculation had no effect on
establishing the stability boundary, because damping at the least
stable inter-blade phase angle was used for all of the eight-bladed
calculations .

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NASA CR 179512

Four- Bladed Comparisons - The six cases were also analyzed for the
four-bladed configuration to assess blade interaction effects. The
predicted damping and frequency for the first four modes are shown
in Figures 19 through 24. The figures show predicted first mode
instability to occur at the wind tunnel Mach numbers summarized in
Table VII. A review of the predicted eight and four-bladed flutter
Mach numbers in Tables V and VII show that the four-bladed
configuration is predicted to be stable at higher Mach numbers than
the eight-bladed configuration, which is in agreement with the test
results. Unfortunately, the variations in predicted stability due
to the variations in predicted modal data, discussed previously
with the eight-bladed configuration, are also transferred to the
four-bladed stability predictions.

The predictions listed in Table VII are compared to test results
in Figure 25. From this Figure it is clear that cases 3, 4, and 6
are in good agreement with the test results, while cases 1 and 2
show low predicted stability, and finally, case 5 is out of
agreement with all the other predictions, as well as the test
results as occurred with eight blades.

Earlier, it was mentioned that the in vacuo frequency predictions
did not correlate- well with wind tunnel test results, and that part
of the discrepancy was due to steady state aerodynamic effects.

The effect that unsteady aerodynamic forces have on the blade
frequency is shown in Table VII. Aerodynamic forces tend to raise
the predicted first mode frequency by approximately 60 Hz at the
flutter conditions. This represents a 30% increase in the first
mode frequency, which brings it in agreement with the measured
values. A review of Table IV and Figures 19 through 24 shows that
the second mode frequency is lowered by approximately 30 Hz due to
aerodynamic effects. This is also in the direction of better
agreement with the test results shown in Figure 9. It is evident,
for this blade, that unsteady aerodynamic forces significantly
alter the natural frequencies of the blades.

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4.0 CONCLUSIONS AND RECOMMENDATIONS

Based on the F203 analytical prediction results and comparisons to

experimental data for the SR—3C-X2 and SR— 3C— 3 model Prop— Fans, the

following conclusions and recommendations are made concerning

Prop-Fan unstalled flutter analysis.

1) The F203 modal aeroelastic stability analysis was effective as a
design tool in developing the SR— 3C— X2 and the SR— 3C— 3 Prop— Fan
models.

2) Pre-test F203 stability predictions for the SR-3C-X2 and SR-3C-3
were confirmed when the SR-3C-X2 fluttered and the SR-3C-3 did
not flutter.

3) Positive first mode torsion-bending coupling is a destabilizing
factor on Prop-Fan unstalled flutter stability and the
minimization of this parameter will increase Prop-Fan stability.

4) The SR-3C-X2 eight-bladed configuration was predicted to be
less stable than the four-bladed configuration in agreement
with test data.

5) Both test data and F203 calculations show that unsteady
aerodynamic loads alter the SR-3C-X2 blade in vacuo natural
frequencies at rotating conditions.

6) Calculated blade modal properties varied significantly with the
structural analysis used, and these variations are reflected in
the F203 calculations.

7) The modal characteristics of the SR-3C-X2 need to be re-examined
both analytically and experimentally to better assess the F203
aeroelastic stability analysis.

8) A polarity difference found between the predicted and measured
least stable inter-blade phase angles warrants further
investigation .

13/14

NASA CR 179512

5.0 REFERENCES

1. Weisbrich, A. L. , J. Godston, and E. Bradley "Technology and
Benefits of Aircraft Counter Rotation Propellers", NASA
CR-168258, December 1982

2. Mehmed, 0., K.R.V. Kaza, J. F. Lubomski, and R. E. Kielb,
"Bending-Torsion Flutter of a Highly Swept Advanced Turboprop",
NASA Technical Memorandum 82975, 1982

3. Turnberg, J. E., "Classical Flutter Stability of Swept
Propellers", 83-0847-CP, AIAA/ASME/ASCE/AHS 24th Structures,
Structural Dynamics and Materials Conference, May 2-4, 1983

4. Elchuri, V., G.C.C. Smith, "Flutter Analysis of Advanced
Turbopropellers", 83-0846-CP, AIAA/ASME/ASCE/AHS 24th
Structures, Structural Dynamics and Materials Conference,

May 2-4, 1983

5. Bansal, P. N. , P. J. Arseneaux, A. F. Smith, J. E. Turnberg, and
B. M. Brooks, "Analysis and Test Evaluation of the Dynamic
Response of Three Advanced Turboprop Models", NASA CR-174814,
August 1985.

6. Rohrbach, C., F. B. Metzger, D. M. Black, and R. M. Ladden,
"Evaluation of Wind Tunnel Performance Testings of an Advanced
45“ Swept Eight-Bladed Propeller at Mach Numbers from 0.45 to
0.85," NASA CR 3505, March 1982

7. Smith, A. F. and B. M. Brooks "Dynamic Response Test of an
Advanced Composite Prop-Fan Model" NASA CR-179528, 1986.

8. Sullivan, William E., Jay E. Turnberg, John A. Violette
"Large-Scale Advanced Prop-Fan (LAP) Blade Design", NASA CR
174790, 1985.

9. Mehmed, 0. and K.R.V. Kaza, "Classical Flutter Experiment Using
a Composite Advanced Turboprop Model", NASA TM 88792, July
1986.

15/16

NASA CR 179512

TABLE I

CALCULATED NATURAL FREQUENCIES FOR THE
COMPOSITE SR-3C MODEL PROP-FANS*

Frequency - Hz (Zero RPM/8636 RPM>

Mode

SR-3C-X2

SR-3C-3

SR-3C-X7

1

189/230

194/242

195/244

2

380/411

448/506

454/484

3

687/704

640/739

717/806

4

744/889

876/963

868/932

5

1074/1073

1122/1183

1138/1151

6

1149/1117

1202/1225

1240/1282

*Furnished by NASA-Lewis

17

NASA CR 179512

TABLE II

COMPARISON BETWEEN CALCULATED AND MEASURED
NATURAL FREQUENCIES FOR THE SR-3C-X2
COMPOSITE MODEL PROP-FAN AT ZERO RPM

Frequency ~ Hz

Mode

1

2

3

4

Calculated

189

380

687

744

Measured*
188 - 208
367 - 387
666 - 696
699 - 728

*Range of measured frequencies for all eight blades tested.
Measurements and calculations performed by NASA-Lewis.

18

NASA CR 179512

TABLE III

SUMMARY OF RUNS AND ANALYSIS CASES FOR THE
SR-3C-X2 ANALYSIS

Analysis Conditions

Analysis Procedure

Mach*

Analysis

i

NAS TRAN

Steady

No. of

RPM

£3/4

NO.

Case

Type

Airloads

Blades

4

8636

58.0

1

Cosmic

No

8

4

2

Cosmic

No

8

4

6100

61.6

:

0.6

3

MSC

No

8

i

i

1

4

4

MSC

1

Yes

8

j

4

7368

61.6

in

•

o

5

MSC

j

Yes

}

8

!

4

6400

56.6

0.6

6

MSC

i

!

Yes

8

*Mach no. only valid with steady airloads.

19

PREDICTED BLADE NATURAL FREQUENCIES
FOR THE SR-3C-X2 MODEL PROP-FAN*

o

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20

PREDICTED AND MEASURED FLUTTER STABILITY FOR THE
SR-3C-X2 IN AN EIGHT-BLADED CONFIGURATION

T5

N

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21

TABLE VI

PREDICTED EIGENVECTORS FOR TWO SR-3C-X2 CONDITIONS

Case 6 Mach 0.6 6400 RPM

135 * interblade phase angle

Mode

Eigenvector

Coupling to Mode 1

1

0.3391

0 . 9169i

100

2

-0.1170

+

0. 1012i

15

3

-0.0594

+

0. 0622i

9

4

-0.0210

+

0. 0197i

3

5

-0.0065

+

0. 0070i

1

6

-0.0002

+

0. 0002i

0

Case 5 Mach 0.5 7386 RPM
135° interblade phase angle

Mode

Eigenvector

Coupling to Mode 1

1

0.06352

-

0 . 9980i

100

2

-0.2652

-

0 . 0883 i

28

3

-0.0756

+

0 . 0655i

10

4

0.0395

-

0 . 0311i

5

5

0.0149

-

0. 0140i

2

6

0.0001

+

O.OOOli

0

22

PREDICTED AND MEASURED FLUTTER STABILITY FOR THE SR-3C-X2
IN A FOUR-BLADED CONFIGURATION

N

73

a

0 )

•

P

X l

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o •

CO

P

a <u

0 )

a p

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< Pm

cm

CM

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CM

CM

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3 X
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ftf • ,
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23/24

PITCH CHANGE AXIS

FIGURE 2 DEFINITION OF MODAL DISPLACEMENTS FOR TORSION-BENDING
COUPLING

26

FIGURE 3 GRAPHITE PLY ORIENTATIONS FOR THREE COMPOSITE SR-3 MODEL
PROP-FANS

Calculated

28

FIGURE

Calculated

29

FIGURE

C\J !■ —

OO X X

I I I
CJCJO

on on on
l l l

cccr cc
cncnon

0 © <

o

o o o o o o o

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I I

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Eh O <
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H O 55
P4 U H

31

c\jr^
cnx x
l l I
uuu
cn co cn
i l i

cccro:

cncncn

a © <

o

oiibd ONidwua snoosiA

32

FIGURE 8 PREDICTED FIRST MODE DAMPING FOR THREE PROPOSED COMPOSITE
SR- 3 MODEL PROP-FANS OPERATING AT 8636 RPM, B 3 / 4 = 58’.

FREQUENCY - HZ

1000

800

600

400

200

0

FIGURE 9

“ PRE-TEST CALCULATION

X - NON-ROTATING TEST

“ 8X6 WIND TUNNEL TEST FREQUENCY RANGE

COMPARISON BETWEEN PRE-TEST IN VACUO NATURAL FREQUENCY
PREDICTIONS WITH MEASURED BLADE NATURAL FREQUENCIES IN AIR

VISCOUS DAMPING RATIO

VISCOUS DAMPING RATIO

0.4

0 MODE 1

WIND TUNNEL MACH NUMBER

FIGURE 13 SR-3C-X2 STABILITY PREDICTION FOR AN EIGHT-BLADED
CONFIGURATION USING CASE 3 MODAL DATA AT 6100 RPM,
B 3 / 4 - 61.6°, MSC NASTRAN, NO STEADY AIRLOADS

37

VISCOUS DAMPING RATIO

VISCOUS DAMPING RATIO

ROTATIONAL SPEED

lOOOO i-

8 BLADES

8000 L

Q-

Q£

© 5

6000

CALCULATION
CASE NUMBER

4000 _

test CALCULATI ON 63/4

O # 56.6°

2000 r O # 61.6°

ADDITIONAL TEST DATA

o

(J

0L

0

CASE NO. = n

0.2

— 1 1_

0.4 0.6

_i _j

0.8 1.0

WIND TUNNEL MACH NUMBER

FIGURE 17 A COMPARISON BETWEEN MEASURED AND PREDICTED SR-3C-X2
BLADE STABILITY IN AN EIGHT-BLADED CONFIGURATION

41

VISCOUS DAMPING RATIO

INTERBLADE PHASE ANGLE - DEG

FIGURE 18 PREDICTED INTERBLADE PHASE ANGLE FOR THE SR-3C-X2 USING
CASE 6 MODAL DATA AT 6400 RPM 8 BLADES

42

VISCOUS DAMPING RATIO

Q MODE 1
0 MODE 2
a MODE 3
a MODE 4

0.4 O.S 0.6 0.7 0.8 0.9 1.0 1.1

WIND TUNNEL MACH NUMBER

D MODE 1
0 MODE 2
a MODE 3
a MODE 4

>“

y 600.0

0.4 0.5 0.6 0.7 0.8 0.9

WIND TUNNEL MACH NUMBER

1.0 l.l

FIGURE 20 SR-3C-X2 STABILITY PREDICTION FOR A FOUR-BLADED

CONFIGURATION USING CASE 2 MODAL DATA AT 6100 RPM

a MODE 1
0 MODE 2
^ MODE 3
MODE 4

3.7

0.8

0.9 1.0

1.1

MACH NUMBER

a MODE 1
© MOOE 2

* MODE 3

* MODE 4

.7 0.8 0.9 1.0 1.1

MACH NUMBER

1CTI0N FOR A FOUR-BLADED
E 3 MODAL DATA AT 6100 RPM

5

VISCOUS DAMPING RATIO

□ MODE 1
0 MODE 2
a MODE 3
a MODE 4

1200.0

a mode l

0 MODE 2
a MODE 3
a MODE 4

0.3 0.4

0.5 0.6 0.7 0.8 0.9

WIND TUNNEL MACH NUMBER

FIGURE 22 SR-3C-X2 STABILITY PREDICTION FOR A FOUR-BLADED

CONFIGURATION USING CASE 4 MODAL DATA AT 6100 RPM

46

VISCOUS DAMPING RATIO

0 MODE 1
0 MODE 2
* MODE 3
f MODE 4

0 MODE 1
0 MODE 2
* MODE 3
o MODE 4

VISCOUS DAMPING RATIO

a MODE 1
0 MODE 2
a MODE 3
a MODE 4

WIND TUNNEL MACH NUMBER

□ MODE x
® MODE 2
a MODE 3
a MODE 4

WIND TUNNEL MACH NUMBER

FIGURE 24 SR-3C-X2 STABILITY PREDICTION FOR A FOUR-BLADED

CONFIGURATION USING CASE 6 MODAL DATA AT 6400 RPM

48

ROTATIONAL SPEED - RPM

lOOOO

8000

6000

4000

2000

0

FIGURE 25

FOUR BLADES

CALCULATION
CASE NUMBER

TEST CALCULATION

O 'O

0.2

61.6°

56.6°

0.4

0.6

0.8 1.0

WIND TUNNEL MACH NUMBER

A COMPARISON BETWEEN MEASURED AND PREDICTED SR-3C-X2
BLADE STABILITY IN A FOUR-BLADED CONFIGURATION

49/50